The ultimate purpose of our research is to understand the important metabolic processes taking place in the human cell. Our research at CSUDH has so far focused on the study of passive transport in in homogeneous media. We have developed an inovative approach based on a combination of mathematical techniques (renormalization, random walks, fluctuation-dissipation), new geometrical concepts (quasi-fractals), and computer simulations (Monte Carlo, Brownian dynamics) to study this topic. This work has now led us to study active transport. In this proposal, we intend to describe how cellular cargo diffuses through the viscous regions of the cell, how it is transported by molecular motors in the cytoskeleton, and how these types of transport are connected at the cellular level. Also, the cell is a dynamic structure and its inherent motion affects the transpot phenomena taking place inside. In order to integrate all these aspects, we will study the motion of particles while driven by thermal fluctuations on suitable dynamical and geometrical models of the cell. We will extend our general formalism to include active trasport and time distributions to represent the random nature and dynamics of the cell.